Preserve input types for various rules (#89)

* Make Float32 stable for both arguments

* revert :NaN change

* remove float guard

* Removed spurious NaN

Author: ptiede

src/rules.jl

@@ -85,7 +85,7 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
 @define_diffrule Base.atan(x, y)    = :( $y / ($x^2 + $y^2)                                 ), :( -$x / ($x^2 + $y^2)                                                     )
 @define_diffrule Base.hypot(x, y)  = :( $x / hypot($x, $y)                                      ), :(  $y / hypot($x, $y)                                                     )
 @define_diffrule Base.log(b, x)    = :( log($x) * inv(-log($b)^2 * $b)                          ), :( inv($x) / log($b)                                                       )
-@define_diffrule Base.ldexp(x, y)  = :( exp2($y)                                                ), :NaN
+@define_diffrule Base.ldexp(x, y)  = :( oftype($x, exp2($y))                                                ), :NaN
 
 @define_diffrule Base.mod(x, y)    = :( z = $x / $y; ifelse(isinteger(z), oftype(float(z), NaN), one(float(z))) ), :(  z = $x / $y; ifelse(isinteger(z), oftype(float(z), NaN), -floor(float(z))) )
 @define_diffrule Base.rem(x, y)    = :( z = $x / $y; ifelse(isinteger(z), oftype(float(z), NaN), one(float(z))) ), :(  z = $x / $y; ifelse(isinteger(z), oftype(float(z), NaN), -trunc(float(z))) )
@@ -296,14 +296,14 @@ _abs_deriv(x) = signbit(x) ? -one(x) : one(x)
 @define_diffrule LogExpFunctions.logmxp1(x) = :((1 - $x) / $x)
 
 # binary
-@define_diffrule LogExpFunctions.xlogy(x, y) = 
+@define_diffrule LogExpFunctions.xlogy(x, y) =
     :(log($y)),
     :(z = $x / $y; iszero($x) && !isnan($y) ? zero(z) : z)
 @define_diffrule LogExpFunctions.logaddexp(x, y) =
     :(exp($x - LogExpFunctions.logaddexp($x, $y))), :(exp($y - LogExpFunctions.logaddexp($x, $y)))
 @define_diffrule LogExpFunctions.logsubexp(x, y) =
     :(z = LogExpFunctions.logsubexp($x, $y); $x > $y ? exp($x - z) : -exp($x - z)),
     :(z = LogExpFunctions.logsubexp($x, $y); $x > $y ? -exp($y - z) : exp($y - z))
-@define_diffrule LogExpFunctions.xlog1py(x, y) = 
+@define_diffrule LogExpFunctions.xlog1py(x, y) =
     :(log1p($y)),
     :(z = $x / (1 + $y); iszero($x) && !isnan($y) ? zero(z) : z)